Vector spaces

[bamby]

Can you, please help me with this problem?

 

If these two operations are defined as follows. With these new definitions, is R³ a vector space?

a) (x₁, y₁, z₁)+(x₂, y₂, z₂)=(x₁ + x₂ + 2, y₁ + y₂ + 2, z₁ + z₂ + 2)

c(x, y, z)=(cx, cy, cz)

 

b) (x₁, y₁, z₁)+(x₂, y₂, z₂)=(x₁ + x₂ + 4, y₁ + y₂ + 4, z₁ + z₂ + 4)

c(x, y, z)=(cx + 4c – 4, cy + 4c – 4, cz + 4c – 4)

 

Thanks!

Edited November 16, 2011 by bamby

[timo]

Just check if the axioms of a vector space are satisfied.

Edited November 16, 2011 by timo

[bamby]

I can't. I know that the first one is a vector space and the second one is not but I can't prove it.

[timo]

You should have read the homework rules which, if I remember it correctly, state somewhere that you are not supposed to be given the answer without showing what you have tried. Despite my hint you haven't even listed up the vector space axioms, less showed your attempts to test them. I don't think there is much to help you at this point.